The trust said it was opposed to a proposal put forward in March by the director general, Mark Thompson, as part of a wide-ranging strategy review.

However, the BBC Trust said it would accept a formal management proposal for the closure of 6 Music's digital sister station, BBC Asian Network, provided that it included alternative plans for meeting the needs of this ethnic minority audience "in different ways".

It said 6 Music was encouraging the take-up of digital radio among listeners, describing it as a "highly distinctive" service that represents "value for money" and is "well liked" by its audience.

The BBC Trust said there had been "significant public support for the service" and that 78% of nearly 50,000 online responses to a consultation on the BBC's future focused on 6 Music. The trust also received more than 25,000 emails and nearly 250 letters about the station, "the great majority" of which opposed the closure plan.

It said BBC managers should be increasing 6 Music's average audience of around 600,000 weekly listeners rather than shutting the station down.

The trust also said 6 Music does not represent a threat to commercial competitors. "Throughout the period of our consultation we have received no evidence from the commercial radio sector to suggest that 6 Music represents any kind of threat either now or in the future, so long as it remains true to its distinctive remit."

BBC executives should consider the future of 6 Music as part of a wider examination of how best to improve the performance of its network of digital radio stations.

"The trust concludes that, as things stand, the case has not been made for the closure of 6 Music," the trust ruled. "The executive should draw up an overarching strategy for digital radio. If the director general wanted to propose a different shape for the BBC's music radio stations as part of a new strategy, the trust would consider it. The trust would consider a formal proposal for the closure of the Asian Network, although this must include a proposition for meeting the needs of the station's audience in different ways."

Ruling on the other elements of Thompson's strategic review of the BBC's activities, the trust said it endorsed the proposal to cut the corporation's online budget by 25%, contingent on being able to "understand and approve the editorial changes involved".

"The BBC should sharpen online's focus so that it is truly distinctive and has clearer editorial vision and control," the trust added.

Thompson's plan to close Blast!, a cross-media service aimed encouraging the creative skills of teenagers, was supported by the trust. The BBC's governing body said it would leave the decision on the future of BBC Switch, the cross-media brand providing content for younger viewers, to management.

On Thompson's proposals for the BBC's TV networks, the trust said it saw no need "for radical changes to the current portfolio". "But the BBC needs to identify future tipping points where reassessment of the structure will become necessary, such as full digital switchover in 2012 and 50% of viewing on a non-linear basis. The BBC has more to do to ensure programmes are truly high quality and distinctive."

Sir Michael Lyons, the BBC Trust chairman, said: "The director general presented us with a thoughtful set of proposals earlier this year in support of a clear future vision for the BBC – a vision the trust supports because it is rooted in the BBC's enduring mission to inform, educate and entertain audiences with programmes and services of high quality, originality and value.

"In order to deliver that vision we have concluded that the BBC must accelerate changes to its behaviour, leading to a clearer definition of the boundaries within which it operates as it makes the transition to the digital future.

"The end result will be a BBC that focuses on its two main obligations to the public – to provide distinctive public service content and to use their money wisely."

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